Generalized Principal Component Analysis
Many problems in computer vision, image processing and machine learning can be formulated as the problem of clustering data points sampled from multiple linear structures in the high-dimensional feature space. The solution to the later problem requires both segmentation of the data points (clustering) and characterization of the linear structures (identification), which is usually considered as a chick-and-egg problem that can only be solved using iterative approach. Working with our collaborators in University of Illinois at Urbana-Champaign (Prof. Yi Ma) and Johns Hopkins University (Prof. Rene Vidal), we developed a non-iterative algorithm for solving the problem of data clustering using multiple linear models. This powerful algorithm is termed Generalized Principal Component Analysis (GPCA) as it can be considered as a generalization of the well-known PCA by fitting the data points using multiple low-dimensional linear models. This algorithm has been applied to solve many fundamental problems in computer vision (e.g., motion segmentation and video/image segmentation), image processing (e.g., representation and compression), and system theory (e.g., hybrid system identification).
Project Researchers
Project Publications
Publications |
Lee Cooper, Jun Liu, Kun Huang, "Spatial segmentation of temporal texture using mixture linear models", Proceedings of the Dynamical Vision Workshop in the International Conference of Computer Vision, 2005. |
Kun Huang, Yi Ma, René Vidal, "Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications", Proceedings of the 2004 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'04), 2004: pp. 631-638. |
Tech Reports |
Kun Huang, Andrew Wagner, Yi Ma, "Hybrid linear system identification via subspace embedding and segmentation", Issued: 2004-12-01 |
Kun Huang, Allen Y. Yang, Yi Ma, "Image representation with hybrid and adaptive linear models", Issued: 2004-10-01 |